1. Noncommutative correspondence categories.

Roughly, in this article I am trying to functorially relate a version of the correspondence category in NCG after Connes-Consani-Marcolli to its counterpart in NCG in a DG setting as outlined in the notes below.

Preprints:

1. Noncommutative tori and the Riemann-Hilbert correspondence (with W. D. van Suijlekom), arXiv:0705.1076.

Survey articles:

1. Noncommutative geometry in the framework of differential graded categories, to appear in the proceedings volume of AGAQ Istanbul, 2006, arXiv:0805.1628.

2. Lecture notes on non-commutative algebraic geometry and noncommutative tori, "An Invitation to Noncommutative Geometry", the proceedings volume of the "International Workshop on NCG", IPM Tehran, 2005, arXiv:math/0610043.

Not intended for publication:

1. On some approaches towards non-commutative algebraic geometry (survey), arXiv:math/0501166.

2. Algebraic and rational points on cubic surfaces (after D. F. Coray), undergraduate thesis. [pdf,ps]